Heaps and Priority Queue Quiz
40 comprehensive questions exploring heap data structures — with 16 code examples covering heap operations, array representation, building heaps, priority queues, heap sort, and advanced variants in this cpp quiz.
40 Questions
~80 minutes
1
Question 1
What is a heap data structure?
A
A specialized tree-based data structure that satisfies the heap property, where each node is greater than or equal to (max-heap) or less than or equal to (min-heap) its children, enabling efficient access to the highest or lowest priority element
B
A linear data structure
C
A graph data structure
D
A hash table variant
2
Question 2
What is the difference between a min-heap and max-heap?
text
Min-heap: parent <= children
Max-heap: parent >= childrenA
A min-heap ensures the smallest element is at the root with each parent smaller than or equal to its children, while a max-heap ensures the largest element is at the root with each parent larger than or equal to its children
B
They are identical
C
Min-heaps have no ordering
D
Max-heaps have no ordering
3
Question 3
How does heap insert operation work?
A
Add the new element at the end of the heap array, then perform heapify-up (bubble up) by comparing with parent nodes and swapping if necessary to maintain the heap property, ensuring the element reaches its correct position
B
Insert at the beginning
C
Insert randomly
D
Heap insert doesn't maintain order
4
Question 4
What is the time complexity of heap insert?
text
Insert: O(log n) worst case
Bubble up through heightA
O(log n) in the worst case due to the heapify-up operation that may traverse from leaf to root, with the heap height being logarithmic, making insertion efficient even for large heaps
B
O(1)
C
O(n)
D
O(n log n)
5
Question 5
How does heap extract-min/max work?
A
Remove the root element (min/max), replace it with the last element in the array, then perform heapify-down by comparing with children and swapping to restore the heap property throughout the tree
B
Remove a random element
C
Remove from the middle
D
Extract doesn't maintain heap property
6
Question 6
What is heapify-down operation?
cpp
Compare with children
Swap with smallest/largest child
Recur until heap property satisfiedA
A recursive process that starts at a node and ensures the heap property by comparing the node with its children, swapping with the appropriate child if the property is violated, then continuing down the tree until the property is restored
B
Moving elements up the heap
C
Removing elements
D
Heapify-down doesn't exist
7
Question 7
What is the time complexity of heap extract operation?
A
O(log n) due to the heapify-down operation that may traverse from root to leaf in the worst case, with the heap height determining the maximum number of comparisons and swaps needed
B
O(1)
C
O(n)
D
O(n log n)
8
Question 8
How are heaps represented in arrays?
cpp
Root at index 0
Left child: 2*i + 1
Right child: 2*i + 2
Parent: (i-1)/2A
Heaps are stored in contiguous arrays with the root at index 0, left child of node i at index 2*i+1, right child at 2*i+2, and parent of node i at index (i-1)/2, enabling efficient memory usage and cache-friendly access
B
Heaps use linked structures
C
Elements are stored randomly
D
Arrays cannot represent heaps
9
Question 9
What is the memory efficiency of array-based heaps?
A
Array-based heaps use O(1) extra space per element with no pointers needed, providing better memory efficiency and cache performance compared to pointer-based tree implementations, especially for large heaps
B
They use more memory than linked structures
C
They require additional pointers
D
Array heaps are memory inefficient
10
Question 10
How do you calculate parent index from child index in heap arrays?
cpp
Parent of i: (i-1)/2
Integer division for floorA
The parent index of any node i (except root) is calculated as (i-1)/2 using integer division, which correctly maps children back to their parents in the array representation of complete binary trees
B
Parent is always at index 0
C
Parent calculation is i/2
D
Parent index cannot be calculated
11
Question 11
What is the build-heap algorithm?
A
An efficient algorithm that constructs a heap from an unsorted array by starting from the last non-leaf node and performing heapify-down on each node moving upwards, achieving O(n) time complexity instead of O(n log n)
B
Inserting elements one by one
C
Sorting the array first
D
Build-heap doesn't exist
12
Question 12
What is the time complexity of build-heap?
text
Build-heap: O(n)
Better than n log n insertionsA
O(n) because the heapify operations at each level take time proportional to the number of nodes at that level times the height, resulting in linear time overall despite the logarithmic factors
B
O(n log n)
C
O(log n)
D
O(n²)
13
Question 13
How does top-down heap construction differ from bottom-up?
A
Top-down construction inserts elements one by one using heap insert operations, resulting in O(n log n) time, while bottom-up construction performs heapify-down from the bottom, achieving O(n) time for better efficiency
B
They are identical
C
Top-down is faster
D
Bottom-up doesn't work
14
Question 14
What is a priority queue?
text
Priority queue: ordered access
Highest/lowest priority firstA
An abstract data type that provides access to the element with the highest (or lowest) priority, supporting insert operations and extract-min/max operations, commonly implemented using heap data structures
B
A queue with random access
C
A stack variant
D
A list with no ordering
15
Question 15
How do heaps implement priority queues?
A
Heaps implement priority queues by storing elements with their priorities, using the heap property to keep the highest/lowest priority element at the root, enabling O(log n) insert and extract operations
B
Heaps cannot implement priority queues
C
Using arrays only
D
Using linked lists
16
Question 16
What is heap sort algorithm?
cpp
Build max-heap
Repeatedly extract max
Place at end of arrayA
An in-place sorting algorithm that first builds a max-heap from the input array, then repeatedly extracts the maximum element and places it at the end of the array, resulting in a sorted array with O(n log n) time complexity
B
A comparison-based sort
C
A stable sorting algorithm
D
Heap sort doesn't exist
17
Question 17
Why is heap sort O(n log n)?
A
Heap sort achieves O(n log n) time complexity because building the initial heap takes O(n) and each of the n extract operations takes O(log n), giving the optimal comparison-based sorting bound
B
Because it uses nested loops
C
Because it compares all elements
D
Heap sort is O(n)
18
Question 18
What is the space complexity of heap sort?
text
In-place sorting
O(1) auxiliary spaceA
O(1) auxiliary space since heap sort performs all operations within the input array itself, rearranging elements in-place without requiring additional storage proportional to input size
B
O(n) space
C
O(log n) space
D
O(n log n) space
19
Question 19
How does heap sort compare to quicksort?
A
Heap sort provides O(n log n) worst-case performance with O(1) auxiliary space but is not stable and has higher constant factors, while quicksort is often faster in practice but has O(n²) worst-case without randomization
B
Heap sort is always faster
C
Quicksort is always faster
D
They have identical performance
20
Question 20
What is a binomial heap?
text
Collection of binomial trees
Efficient merge operationsA
An advanced heap variant consisting of a collection of binomial trees that allows efficient merging of heaps in O(log n) time, supporting decrease-key and delete operations faster than binary heaps
B
A binary heap variant
C
A heap with two elements
D
Binomial heaps don't exist
21
Question 21
What is a Fibonacci heap?
A
An advanced heap variant that supports decrease-key operations in O(1) amortized time and extract-min in O(log n) amortized time, using a more complex tree structure with lazy deletion for improved performance in algorithms like Dijkstra's
B
A heap using Fibonacci numbers
C
A binary heap variant
D
Fibonacci heaps don't exist
22
Question 22
What is a d-ary heap?
text
Each node has d children
Reduces height for large dA
A generalization of binary heaps where each node has d children instead of 2, reducing tree height and potentially improving cache performance for certain values of d, though increasing the cost of finding the minimum child
B
A heap with d elements
C
A binary heap variant
D
d-ary heaps don't exist
23
Question 23
How do heap variants compare in performance?
A
Binary heaps provide balanced performance with O(log n) for all operations, binomial heaps excel at merging with O(log n) amortized merge time, and Fibonacci heaps optimize decrease-key for algorithmic applications requiring frequent priority updates
B
All heap variants have identical performance
C
Binary heaps are always best
D
Advanced variants are slower
24
Question 24
What is heap stability in priority queues?
text
Stable: equal priorities maintain order
Unstable: order may changeA
Heap stability refers to whether elements with equal priorities maintain their relative insertion order, with binary heaps being unstable due to heapify operations that may reorder equal elements, requiring additional mechanisms for stable priority queues
B
Heaps are always stable
C
Stability doesn't matter
D
Heaps cannot be stable
25
Question 25
How do comparators work in heap-based priority queues?
A
Comparators define the priority ordering by providing a comparison function that determines whether one element has higher priority than another, enabling custom ordering beyond natural ordering for complex priority schemes
B
Comparators sort the heap
C
Comparators are not used
D
Comparators define element values
26
Question 26
What are the applications of priority queues in scheduling?
text
OS process scheduling
Event simulation
Task managementA
Priority queues enable efficient scheduling in operating systems for process management, discrete event simulation for handling events in chronological order, and task management systems where urgent tasks are processed first
B
Priority queues cannot be used for scheduling
C
Only for sorting
D
Only for searching
27
Question 27
How does heap height affect performance?
A
Heap height determines the worst-case time complexity of insert and extract operations, with lower height providing better performance, which is why d-ary heaps with higher branching factors can improve performance for certain access patterns
B
Height has no effect
C
Higher height is better
D
Height affects memory only
28
Question 28
What is the heap property formally?
text
For max-heap: A[parent] >= A[child]
For min-heap: A[parent] <= A[child]A
The heap property requires that for every node i, the value at i is greater than or equal to (max-heap) or less than or equal to (min-heap) the values at its children, ensuring the root contains the extreme value
B
No ordering requirements
C
Only leaves must be ordered
D
Heap property is random
29
Question 29
How do heaps handle duplicate values?
A
Heaps handle duplicates naturally through the heap property, allowing multiple elements with the same value while maintaining the required ordering, though stability may be affected depending on the implementation
B
Duplicates are not allowed
C
Duplicates break the heap
D
Duplicates are removed
30
Question 30
What is the practical branching factor for d-ary heaps?
text
d typically 3-8
Balances find-min and heightA
The branching factor d is typically chosen between 3 and 8 to balance the cost of finding the minimum child (which increases with d) against the benefit of reduced height, optimizing for specific memory hierarchies and access patterns
B
Always d=2
C
Always d=100
D
Branching factor is not relevant
31
Question 31
How do Fibonacci heaps achieve fast decrease-key?
A
Fibonacci heaps achieve O(1) amortized decrease-key by using a lazy approach where decreased nodes are cut from their parents and marked, with cascading cuts performed during extract-min to maintain the heap property
B
By using binary trees
C
By rebuilding the heap
D
Fibonacci heaps don't have fast decrease-key
32
Question 32
What is the amortized analysis of heap operations?
text
Amortized: average over sequence
Accounts for infrequent expensive operationsA
Amortized analysis considers the average cost of operations over a sequence, accounting for the fact that expensive operations are infrequent and their cost is distributed across many cheap operations, providing a more accurate performance measure
B
Same as worst-case analysis
C
Always better than worst-case
D
Amortized analysis doesn't exist
33
Question 33
How do heaps support decrease-key operations?
A
Decrease-key operations are supported by reducing an element's priority and performing heapify-up to restore the heap property, though this is less efficient in basic heaps compared to advanced variants like Fibonacci heaps
B
Heaps don't support decrease-key
C
Decrease-key requires rebuilding
D
Only increase-key is supported
34
Question 34
What is the cache performance of array-based heaps?
text
Contiguous memory access
Good spatial localityA
Array-based heaps provide excellent cache performance due to contiguous memory layout and spatial locality, with heapify operations accessing nearby elements that are likely to be in cache, unlike pointer-based implementations
B
Poor cache performance
C
No cache effects
D
Worse than linked structures
35
Question 35
How do binomial heaps support fast merging?
A
Binomial heaps support O(log n) merge operations by combining binomial trees of the same order using simple linking operations, making them suitable for applications that frequently merge priority queues
B
By using binary trees
C
By rebuilding heaps
D
Binomial heaps don't support merging
36
Question 36
What is the trade-off in choosing heap variants?
text
Binary heap: simple, balanced
Advanced: optimized for specific operationsA
Binary heaps offer simplicity and good average performance for all operations, while advanced variants like Fibonacci heaps provide better asymptotic performance for specific operations at the cost of increased implementation complexity
B
No trade-offs exist
C
Advanced variants are always better
D
Binary heaps are always better
37
Question 37
How do heaps handle dynamic priorities?
A
Heaps support dynamic priorities through decrease-key and increase-key operations that adjust element priorities and restore the heap property, enabling applications where priorities change over time like in graph algorithms
B
Heaps don't support dynamic priorities
C
Only static priorities work
D
Dynamic priorities require rebuilding
38
Question 38
What is the heap construction bottleneck?
text
Bottom-up: O(n) optimal
Top-down: O(n log n) suboptimalA
The main bottleneck in heap construction is using top-down insertion approach which gives O(n log n) time instead of the optimal O(n) bottom-up build-heap algorithm that exploits the heap structure more efficiently
B
No bottleneck exists
C
Bottom-up construction is slower
D
Construction is always O(n log n)
39
Question 39
How do heaps compare to sorted arrays for priority queues?
A
Heaps provide O(log n) insert and extract operations with O(1) peek, while sorted arrays offer O(log n) insert but O(1) extract-min, making heaps better for frequent insertions and sorted arrays better for frequent extractions
B
Heaps are always better
C
Sorted arrays are always better
D
They have identical performance
40
Question 40
Considering heap data structures and their implementation challenges, which fundamental property makes heaps essential for efficient priority-based algorithms despite the complexity of maintaining the heap invariant through heapify operations?
A
Heaps guarantee O(log n) access to the priority element while supporting efficient insertions and updates, providing the optimal balance between priority access speed and modification cost that enables algorithms like Dijkstra's shortest path and Huffman coding to achieve their time bounds
B
Guaranteed O(1) performance
C
Minimal memory overhead
D
Simplicity of implementation